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4.1.5 SA Algorithm Performance

Figure 18 shows the progress of a SA search on the two-dimensional Rosenbrock function, . Although one would not ordinarily choose to use SA on a problem which is amenable to solution by more efficient methods, it is interesting to do so for purposes of comparison. Each of the solutions accepted in a 1000 trial search is shown (marked by symbols). The algorithm employed the adaptive step size selection scheme of equations (67) and (68). It is apparent that the search is wide-ranging but ultimately concentrates in the neighborhood of the optimum.

Figure 18: Minimization of the Two-dimensional Rosenbrock Function by Simulated Annealing --- Search Pattern.

Figure 19 shows the progress in reducing the objective function for the same search. Initially, when the annealing temperature is high, some large increases in f are accepted and some areas far from the optimum are explored. As execution continues and T falls, fewer uphill excursions are tolerated (and those that are tolerated are of smaller magnitude). The last 40% of the run is spent searching around the optimum. This performance is typical of the SA algorithm.